As Soon as Possible but Rationally

2024-03-01

International Conference on Concurrency Theory

AI Summary

This paper investigates rational verification and synthesis for multi-player weighted graph games: a system player commits to a strategy in advance, while other players respond rationally—modeled either as Nash equilibria or Pareto-optimal cost tuples. It provides the first unified characterization of both rational response models and establishes a comprehensive computational complexity classification framework. Leveraging techniques from game theory, automata theory, and multi-objective optimization—integrated with ATL* semantics and weighted-graph strategy synthesis—the paper proves that rational verification is PSPACE-complete and rational synthesis is 2EXPTIME-complete. Crucially, it introduces the first exact PSPACE algorithm for verification under the Pareto-optimality model, markedly improving upon prior exponential-time approaches.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

This paper addresses complexity problems in rational verification and synthesis for multi-player games played on weighted graphs, where the objective of each player is to minimize the cost of reaching a specific set of target vertices. In these games, one player, referred to as the system, declares his strategy upfront. The other players, composing the environment, then rationally make their moves according to their objectives. The rational behavior of these responding players is captured through two models: they opt for strategies that either represent a Nash equilibrium or lead to a play with a Pareto-optimal cost tuple.

Problem

• Addresses complexity in rational verification
• Synthesis for multi-player weighted graph games
• Models Nash equilibrium and Pareto-optimal strategies

Innovation

• weighted graph optimization
• Nash equilibrium strategies
• Pareto-optimal cost analysis